Advanced Math/Complex number fallacy.

which means i=0. Can u explain me what went wrong in the above calculation ?(From what i know,taking log for e^2i(pi)is defined, since e^2i(pi)=1 gives [e^2i(pi)] is a real number and thus logarithm is defined) .

>>>>>>>>>>>>>>>>>> No you don't get that. The complex logarithm is defined differently -- it is multiple-valued, sort of like the inverse trig functions.

which means i=0. Can u explain me what went wrong in the above calculation ?(From what i know,taking log for e^2i(pi)is defined, since e^2i(pi)=1 gives [e^2i(pi)] is a real number and thus logarithm is defined) .

There is a cute book on Mathematical Fallacies, which you might look up. Perhaps this belongs there.